Expression of type Lambda

from the theory of proveit.numbers.exponentiation

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, a, x, y
from proveit.logic import And, Equals, InSet
from proveit.numbers import Exp, Less, LessEq, Real, two, zero

# build up the expression from sub-expressions
expr = Lambda([a, x, y], Conditional(LessEq(Exp(y, a), Exp(x, a)), And(InSet(a, Real), InSet(x, Real), InSet(y, Real), And(LessEq(x, y), Less(y, zero)).with_total_ordering_style(), Equals(a, two))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(a, x, y\right) \mapsto \left\{y^{a} \leq x^{a} \textrm{ if } a \in \mathbb{R} ,  x \in \mathbb{R} ,  y \in \mathbb{R} ,  x \leq y < 0 ,  a = 2\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	28, 34, 35
2	Conditional	value: 3 condition: 4
3	Operation	operator: 30 operands: 5
4	Operation	operator: 21 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 10, 11, 12, 13
7	Operation	operator: 15 operands: 14
8	Operation	operator: 15 operands: 16
9	Operation	operator: 19 operands: 17
10	Operation	operator: 19 operands: 18
11	Operation	operator: 19 operands: 20
12	Operation	operator: 21 operands: 22
13	Operation	operator: 23 operands: 24
14	ExprTuple	35, 28
15	Literal
16	ExprTuple	34, 28
17	ExprTuple	28, 25
18	ExprTuple	34, 25
19	Literal
20	ExprTuple	35, 25
21	Literal
22	ExprTuple	26, 27
23	Literal
24	ExprTuple	28, 29
25	Literal
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operands: 33
28	Variable
29	Literal
30	Literal
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	35, 36
34	Variable
35	Variable
36	Literal